Constant Heat Conductivity Research Articles

Normal zone propagation within a superconducting magnetic system and cryostabilization of superconductivity

A theoretical study of normal zone propagation along composite conductors in contact with liquid helium which accounts for the resulting rate of heat release and non-uniformity of heat conduction coefficient is described. The Maddock-James-Norris theorem is shown to be true only for a constant heat conduction coefficient. The formulae are given for the speed of the normal zone propagation. Equations have been obtained which describe the collapse dynamics or normal zone growth within the superconducting magnetic systems; time of collapse and normal zone growth being evaluated. Non-linear heat waves of a new type are assumed to exist in a composite in addition to the solution with an interface of normal and superconducting regions.

Study of the structure of switch-on ionizing shock waves

The Navier-Stokes equations with constant viscosity and heat conductivity coefficients were used. It was found that the condition proposed by Kulikovskii and Lyubimov on the structure of the shock could be used to choose a unique downstream state for a given upstream state which agreed with experimental results for a suitable choice of conductivity, though the results were quite sensitive to changes in the conductivity It was found that this was equivalent to choosing the minimum shock thickness keeping the transverse magnetic field component always the same sign. In the weak shock limit, the condition that the downstream velocity was equal to the slow hydromagnetic wave speed was also found to hold.

On Certain Cases of Simple Exact Solutions of Flow Equations in a Compressible Imperfectly Viscous Fluid with Particular Conditions

In the most general case of flow in a compressible fluid the density, viscosity, specific heat at constant volume, specific heat at constant pressure and heat conductivity are functions of pressure and temperature. The solution of equations of motion together with equation of continuity and of energy present great difficulties. The physical conditions superimpose c'rtain boundary values on velocity, density, pressure and temperature. Because the energy equation expresses only in an analytical way the law of conservation of energy with all its possible forms like intrinsic, kinetic, etc. one more restrictive condition must be superimposed on the whole system. This usually contains the thermodynamic relationship between heat added, intrinsic energy and external work. It may refer also to the value of heat content per unit mass. This picture shows that at the present time the difficulties in the solution of equations are probably insurmountable. But it is possible to select cases satisfying only a part of the restrictive conditions, which although uninterpretable in all details from a physical standpoint, are solvable from a mathematical point of view. In the present paper three such cases are solved under the conditions that the coefficients of viscosity and thermal conduction are constant, that only one boundary condition is superimposed, namely the one concerning the velocity at infinity and that all other restrictive conditions are neglected. The cases are: two-dimensional source, circular vortex, and spiral vortex. The solution was obtained in the form of exponential functions and the worked-out examples represent the cases of exact formal solutions of equations under accepted conditions. This last is the main aim of the paper. The obtained results show that from the four parameters two i.e. velocity and density are always interpretable from a physical standpoint, but two others i.e. temperature and pressure are, in some cases, uninterpretable from a physical standpoint. In certain cases they came out to be negative in the whole plane. The case of a source was reduced to adiabatic conditions. Also the case of a three-dimensional source in adiabatic conditions was solved

The thermal stresses in solid and in hollow circular cylinders concentrically heated

1. The large differences of temperature which exist between the inside and outside of the heating or firing tunnels used in pottery and other works, and between the inner and outer portions of the concrete or masonry pillars supporting the floors of a building in which a fire occurs, make the thermal stresses approach the breaking strength of the materials and they are crushed or torn asunder. The same may be said to a less degree of chimney stacks, and of the walls of the cylinders of internal combustion engines. In order to prevent this, it is necessary to design the structure so as to withstand the stresses which will be produced by the differences of temperature to which they will be subjected. The calculation of these stresses has only been carried out for a hollow cylinder of constant elasticity and heat conductivity, with the temperature throughout it following the steady logarithmic law and the material expanding according to the linear law.